Volume of Horizontal Tank: 10ft. x 18ft.

The more accurate value is 3.1415926535897932384626433832795. If you use this value, the answer is 1413.716817940626237... cu. ft.In summary, to calculate the volume of a cylindrical tank that is on its side, you can use the formula V = (π/4)(D)^2(L), where D is the diameter of the tank and L is its length. Using a more accurate value for pi will result in a more precise answer.
  • #1
jim1174
79
0

Homework Statement



How would you calculate the volume of a cylindrical tank that is on its side (called a horizontal tank)? Calculate the volume if that tank that is 10 ft. in diameter and 18 ft. long. I already know the answer i just need help understanding how they got the answer

Homework Equations

The Attempt at a Solution


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math.jpg
 
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  • #2
jim1174 said:

Homework Statement



How would you calculate the volume of a cylindrical tank that is on its side (called a horizontal tank)? Calculate the volume if that tank that is 10 ft. in diameter and 18 ft. long. I already know the answer i just need help understanding how they got the answer

Homework Equations

The Attempt at a Solution


[/B]
math.jpg

The radius of the tank is equal to half the diameter: d = 10 feet → r = 10/2 = 5 feet.

Since the tank is on its side, its length will be equal to the height of a similar cylindrical tank standing on its end, thus h = length = 10 feet.

Plug numbers into formula, turn crank, out pops volume.

Only, in this case, the factor of 1/3 doesn't belong in the formula for the volume of a cylindrical tank. Are you sure that the tank wasn't in the shape of a cone or conical?
 
  • #3
is this right
volume= pi x (5ft)2 x18
3.14 x 25ft2 x18 ft
35325ft
 
  • #4
jim1174 said:
is this right
volume= pi x (5ft)2 x18
3.14 x 25ft2 x18 ft
35325ft
No. You've multiplied 3.14 by 252 by 18, instead of multiplying 3.14 by 25 by 18.
 
  • #5
jim1174 said:
is this right
volume= pi x (5ft)2 x18
3.14 x 25ft2 x18 ft
35325ft
Also, the units are usually omitted. If you put them in, be consistent. You have units for the radius but left them out for the length of the tank. It should be understood by a reader that the units on the left and right sides are the same; namely, ft3.
 
  • #6
so the correct answer is 3.14 X 25 X18 = 1413ft
 
  • #7
jim1174 said:
so the correct answer is 3.14 X 25 X18 = 1413ft
No, for two reasons.
  1. For a volume with measurements in feet, the volume units are cubic feet.
  2. The correct answer is closer to 1414 cu. ft. Because you used such a crude approximation for ##\pi##, it caused the precision of your calculated volume to be off in the units place.
 
  • #8
this is what is written on my home work sheet
For a cylindrical tank, the formula to determine volume is:Volume = π r2 h where:
π = pi, a mathematical constant that equals approximately 3.14 r = radius of the tank (radius is ½ the diameter)

h = height of the tank

Example: A cylindrical tank is 10 ft. in diameter and 20 ft. tall; what is its volume? r = 1/2d = ½ x 10 ft = 5 ft.

h = 20 ft. Volume = π x (5 ft)2 x 20 ft

= 3.14 x 25 ft.2 x 20 ft

= 1570 ft3
 
  • #9
jim1174 said:
this is what is written on my home work sheet
For a cylindrical tank, the formula to determine volume is:Volume = π r2 h where:
Please do something to indicate that a number is an exponent. The simplest thing to do is to use the ^ symbol, as in πr^2 * h.
jim1174 said:
π = pi, a mathematical constant that equals approximately 3.14 r = radius of the tank (radius is ½ the diameter)

h = height of the tank

Example: A cylindrical tank is 10 ft. in diameter and 20 ft. tall; what is its volume? r = 1/2d = ½ x 10 ft = 5 ft.

h = 20 ft. Volume = π x (5 ft)2 x 20 ft

= 3.14 x 25 ft.2 x 20 ft

= 1570 ft3
Using 3.14 for ##\pi##, the above is the answer you get, but you should be using a better approximation. Most calculators have ##\pi## built in with about 10 decimal place accuracy. Using a more accurate value, the answer is closer to 1571 ft3
 
  • #10
i think i have figured out the answer to my original question
V = ( pi / 4 ) ( D )^2 ( L )

V = ( pi / 4 ) ( 10 ft )^2 ( 18 ft )

V = 450 pi ft^3 = 1413 cu ft
 
  • #11
jim1174 said:
i think i have figured out the answer to my original question
V = ( pi / 4 ) ( D )^2 ( L )

V = ( pi / 4 ) ( 10 ft )^2 ( 18 ft )

V = 450 pi ft^3 = 1413 cu ft
If you round to the nearest cubic foot, it's 1414 cu. ft. Apparently you're still using 3.14 for ##\pi##, which is a very crude approximation.
 

1. How do you calculate the volume of a horizontal tank?

To calculate the volume of a horizontal tank, you need to know the length, width, and height of the tank. In this case, the length is 10ft and the width is 18ft. The formula for calculating volume is length x width x height, so the volume of this tank would be 10ft x 18ft x height. For example, if the height of the tank is 5ft, the volume would be 10ft x 18ft x 5ft = 900 cubic feet.

2. What is the formula for finding the volume of a horizontal tank?

The formula for finding the volume of a horizontal tank is length x width x height. This formula works for any shape of tank, as long as you have the necessary measurements. In this case, the length is 10ft, the width is 18ft, and the height is the unknown value that will determine the volume of the tank.

3. Can you use the same formula to find the volume of any horizontal tank?

Yes, the formula for finding the volume of a horizontal tank (length x width x height) can be used for any horizontal tank regardless of its size or shape. However, make sure to use consistent units for all measurements, such as feet for length, width, and height, to get an accurate volume calculation.

4. How do you convert the volume of a horizontal tank from cubic feet to gallons?

To convert the volume of a horizontal tank from cubic feet to gallons, you need to know the conversion factor. One cubic foot is equal to approximately 7.48052 gallons. So, to convert cubic feet to gallons, you would multiply the volume in cubic feet by 7.48052. For example, if the volume of the tank is 900 cubic feet, the conversion would be 900 x 7.48052 = 6,732.468 gallons.

5. Can the volume of a horizontal tank change over time?

Yes, the volume of a horizontal tank can change over time. This can happen due to factors such as evaporation, leakage, or changes in temperature. It is important to regularly monitor the volume of a tank and make necessary adjustments to ensure accuracy in calculations and prevent any potential issues.

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